In 1947, he began studying aeronautics in the Soviet Union, and he became the general manager of a soda factory in Lukavac in 1958. From 1974 to 1978, he served as Prime Minister of SR Serbia, and then as President of the Assembly from 1978 to 1982.
Following Milošević's purge of the League of Communists of Serbia and unconstitutional consolidation of power within the republic in 1987, the Central Committee of the League of Communists of Yugoslavia responded by holding confidence votes in 1988. Čkrebić, widely viewed as a Milošević ally, was the only sitting member to lose his vote of no confidence; he thereafter resigned from the Committee.[2][3] Milošević himself was exempt from facing a similar vote because he held leadership over the League of Communists of Serbia. Čkrebić thus retired from politics in 1990.